Apparatus for signalling angular displacement

ABSTRACT

To signal the angle displacement of the synchro transmitter or resolver rotor, signals representing products of trigonometrical functions of the supply voltage angle omega t and the rotor angle phi are processed until they can be combined to give a resultant sin ( omega t + OR - phi ) or cos ( omega t + OR phi ) and the resultant is then compared with sin omega t or cos omega t to obtain the rotor angle phi . Parallel integrator and differentiator circuits in the processing unit prevent substantial amplitude change with frequency drift. Frequency doubling circuits are used in such a manner that flyback occurs at a selected submultiple of 180*.

O United States Patent [151 3,648,042

Perrett [4 1 Mar. 7, 1972 [54] APPARATUS FOR SIGNALLING 3,504,361 3/l970Catton ..235/ 186 X LA DISPLACEMENT 3,482,231 12/1969 Florek et al......340/198 3,555,542 1/1971 Guiot ..340/198 X [72] inventor: BrianRaymond Perrett, Radstock, En- 3,521,173 7/1970 Farley ..307/232 X gland3,509,475 4/1970 Parker ..328/133 3,469,196 9 1969 C t l. ..328 133 [731Assignee British Alma Limiled 3,465,256 9/1969 ..328/133 don, England3,464,016 8/1969 Kerwin et al ..328/133 X [22] Filed: Mar. 31, 1970Primary Examiner-Felix D. Gruber [21] Appl. No.: 24,147Attorney-Kemon,lalmer&Estabrook [30] Foreign Application Priority Data[57] ABSTRACT To signal the angle displacement of the synchrotransmitter or Apr. 16, 1969 Great Britain ..l9,435/69 resolver rotorsignals representing products of trigonometri cal functions of thesupply voltage angle wt and the rotor angle US. 83, 86, are processeduntil they can be combined to give a resultant 313/661 sin (mic/t) orcos (wt-12) and the resultant is then compared [51] Int. Cl. "G06g 7/22with sin wt or cos wt to obtain the rotor angle 4). Parallel in- [58]Field of Search ..735/ 183, 186, 189; 307/232, tegrator anddifierentiator circuits in the processing unit 307/295; 328/133, 134,155; 318/654, 661; prevent substantial amplitude change with frequencydrift. 340/198, 347 Frequency doubling circuits are used in such amanner that flyback occurs at a selected submultiple of 180. [56]References Cited 8 Claims 5 Drawing Figures UNITED STATES PATENTS A3,537,018 10/1970 Modiano ...328/133 5/ m 5/!) M 3m 4m- Cam 67/? w).605a. @MZ Q6; K Z/ q W g /0 000M now/r W996 52,

V SM/Mel (71 020 @020 9 -5//; WI, 605 a 2? 26 50 32 4a f s/h/mm) S/DAMM) 5/fl/W/+) Freq, Fre p 1 J @W/Efl I 277 605 ,Sumw 200 (32 0 g g, 207W9? 5/0 WI. 5m. WI Cos wt smi 5/0 Wt C05 II y 46 ,0 a a I w-p 5s(flu/fer 1 001100; 5 Ami/sf l i Patented March 7, 1972 4 Sheets-Sheet lPatented March 7, 1972 3,648,042

4 Sheets-Sheet .J

Patehted March 7, 1972 4 Sheets-Sheet 5 APPARATUS FOR SIGNALLING ANGULARDISPLACEMENT This invention relates to apparatus for signalling theangular displacement of a body about an axis using a synchro transmitteror resolver, the output from which is resolved by electronic means toderive an electric signal representative of the said angulardisplacement.

According to the present invention, we derive from the synchrotransmitter or resolver first and second signals representing twodifferent products of two terms, one of which is a sine or cosinefunction of the supply angle and the other of which is the sine orcosine function of the rotor angle, one of the terms occurring in bothproducts; we then derive from a first of these signals a further signalwhich is the equivalent of the second signal with the sine and cosinefunctions reversed; thereafter we combine the said further signal withthe second signal to obtain a resultant signal representing the sine orcosine of the sum or difference of the supply angle and the rotor angle,and we compare this resultant signal with the corresponding sine orcosine of the supply angle to obtain a signal representing the rotorangle.

The signal indicating the rotor angle will have a flyback every 180, ifit is required that the flyback occurs every 90, for example, the saidresultant signal may be applied to a frequency doubling circuit. Forexample, if the said resultant signal represents the sine of the sum ofthe supply angle and the rotor angle, the output of the frequencydoubling circuit will represent the sine of the rotor angle and twicethe supply signal angle.

In our preferred apparatus embodying the invention, we provide azero-setting means including means generating a pulse for every cycle ofthe supply signal and responsive to the said resultant signal to controlthe pulse phase in accordance with the rotor angle; a capacitorconnected to a constant current charging circuit is discharged insynchronism with the pulses and the capacitor waveform is compared witha reference level by a comparator which generates pulses having amark-space ratio controlled by this comparison. The reference level, theadjustment of which provides the zerosetting facility, is preferablyderived from the peak value of the charging capacitor voltage so thatslow changes in the charging circuit will equally affect the referencelevel and the charging waveform.

As an example, the first and second signals may be sin wt sin (I: andsin to! cos 4; (the term sin to! occurring in both products); from thefirst product signal we derive a further signal cos wt sin ti), which isthe equivalent of the second product signal with the sine and cosinefunctions reversed. We then combine the second signal and the furthersignal to obtain sin (wl+q5).

it is an important feature of the preferred apparatus, that one of thesaid product signals, in which a sine or cosine com ponent has to beconverted to a cosine or sine component, is applied both to anintegrator circuit and, through an inverter circuit, to a differentiatorcircuit, the outputs of the integrator and differentiator being added.Electronic circuits that will produce a 90 phase shift normally cause anoutput amplitude change if the frequency varies. This is a seriousdisadvantage, particularly for an aircraft 400 Hz. supply which maydrift by as much as percent. If our parallel integrator anddifferentiator circuits have similar time constants, the effects of afrequency variation on the two circuits are in opposite senses and theresultant change in amplitude is very small.

In order that the invention may be better understood, one example willnow be described with reference to the accompanying drawings. in thisexample, we used the trigonometrical combination formulas sin A cos B 1cos A sin B sin (AiB). However, the circuit could equally well bedesigned to use only one of these alternatives or to use one or both ofthe relationships cos A cos B i sin A sin B cos (AizB). In the drawings:

FIG. 1 is a block diagram of the apparatus, and

FIGS. 2 to 5 are circuit diagrams of component parts of FIG. 1.

The three stator windings of a synchro transmitter (not shown) provideon lines 10, 12 and 14 signals having the values sin an cos sin wt cos(+21r/3), sin wt cos (+4rr/3) applied across the primary windings ,oftwo transformers T, and T As it has been assumed that a synchrotransmitter provides the input signals, link L2 is closed to provide aScott connection between the two transformer primaries. if a resolverhad provided the input signals link L would have been open and link L,would have been closed.

In either case, the signals derived from the ends of the center-tappedsecondary of transformer T, represent V, sin wt cos and-V, sin wt cos d)respectively. One end of the secondary of transformer T is grounded andthe other end suppliesa potentiometer P,, the wiper of which provides asignal representing V,/2 sin wt sin dz.

We require to convert this latter signal into V,/2 cos wt sin 41, thatis to say sin out has to be changed to sin (mt-)= cos on. However, asexplained above conventional electronic circuits which can produce a 90phase shift result in amplitude variation .in face of frequency drift.An integrator circuit alone, operating on the signal V,/2 sin cut sin 45would give V,/2 l/wT cos wt sin 4) where T is the time constant of theintegrator.

If the frequency to increases by 10 percent, the amplitude of theintegrator output falls by 10 percent. In a similar manner, theinverting and differentiating circuits alone, operating on the sameinput voltage would give V,/2 mT cos w! sin 4) where again T is the timeconstant of the differentiator. In this case if the frequency increasesby 10 percent, the amplitude increases by 10 percent.

By connecting the integrator in parallel with the inverting anddifferentiating circuits and combining their outputs in a subsequentsumming stage, the effect of frequency drift on the amplitude isdrastically reduced. if the time constant T is the same for theintegrating and differentiating circuits, it can be shown that forw=(m,,tAw,,), the amplitude of the summing circuit output will varyapproximately by a factor of Thus, if A m,,==l0% m this 10 percentchange in frequency results in a change in amplitude of only one-halfpercent.

Referring again to the drawing, the signal V,/2 sin wt sin d: from thewiper of potentiometer P, is applied firstly to an integrator circuit 16from which there is obtained an output l/a T cos wt sin (6; and secondlyto an inverter circuit 18 followed by a differentiating circuit 20 fromwhich there is obtained an output equal to -wT cos mt sin If).

The signals from the circuits 16 and 20 are both applied to each of twohalf-Wien summing circuits 22 and 24. The half- 'Wien summing networksare used instead of conventional resistive summing networks to eliminatethe high frequency noise which differentiators tend to emphasize. In thecircuit 22 these two signals are added to the sin wt cos 4) signal fromtransformer T, and in circuit 24 they are added to the sin wt cos ()5signal from the lower end of the secondary of transformer T,.

It has been shown that the signals from circuits l6 and 20, when addedwith suitable scaling factors, are equivalent to cos wt sin 4),therefore the output of the circuit 22 is the sum of sin an cos d: andcos wt sin (1:, namely sin (wt-d1). in a similar way, the output of thesumming circuit 24 is sin(wt+). Thus, in each case a signal has beenobtained which can be compared with the rotor input signal sin wt toprovide an output representing the rotor angle (1:. The signals (sinnit-1b) and sin(wt+) could be used to control opposite inputs of abistable circuit and thereby to control gates permitting the'passage ofpositive or negative DC voltage, so that the output voltage wouldrepresent in amplitude and polarity the amplitude and sense of the angle(L. This signal would increase progressively from to 180 and then wouldthen would fly back to the value it had at 0.

In the present example, it was required to make the output flyback occurevery 45. To do this, the outputs of the two circuits 22 and 24 wereapplied to frequency doubling circuits 26 and 28 respectively. It willbe appreciated that in the resultant expressions for the output signals,only the rotor input voltage phase angle is doubled, so that the outputsof circuits 26 and 28 are sin (Zen-1b) and sin (2wt+). In this examplethe input frequency was 400 Hz. and consequently the frequency of thesignals from the doublers 26 and 28 is 800 Hz. In a similar manner,these signals are again doubled in frequency by the frequency doublingcircuits 30 and 32 to give outputs at a frequency of 1,600 I-Iz.represented by the expressions sin(4wt and sin (4mt+) respectively.

The signals from the frequency doubling circuits 30 and 32 go to triggercircuits 34 and 36. These convert each signal into a train of pulses ofsubstantially square wavefonn. The pulses from trigger circuit 36 godirectly to one side of a bistable circuit 38. The pulses from triggercircuit 34 are applied first to a circuit 40 which provides a set zero"facility which has the same effect as rotating the body of the synchro.The pulses from this set-zero circuit go to the other side of thebistable circuit 38. Opposite outputs of the bistable circuit controlswitches 42 and 44 which are field-effect transistor circuits. Theswitch 42 receives positive DC voltage from the reference andgain-adjusting circuit 45 by way of the buffer 46. The switch 44receives the output of the buffer 46 through an inverter 48 and is thussupplied with negative DC voltage. The output of the switches 42 and 44goes through a low-pass out put filter 50 to the output terminal 52. Asindicated above, the outputs of the circuits 30 and 32 are sinewaveforms whose phase changes completely for 45 rotation of the synchrorotor. Consequently, the output voltage at terminal 52 has a flybackevery 45 of rotation of the synchro rotor. The omission of the secondfrequency doubling circuit in each chain would give an output having afull cycle of variation in a submultiple of 360 variation of the angle 0or stated differently, a flyback every 90 of rotation.

Turning now to the details of the circuits, the integrating circuit 16is of conventional design with a capacitor in the feedback loop aroundan amplifier. The inverter circuit 18 is a conventional invertingamplifier and the differentiating circuit is again of conventional formwith a series capacitor in the input lead and a resistive feedbackconnection connected back to the same input. Such circuits are wellknown and can be found in standard textbooks. The half-Wien summingcircuits are also conventional. The three inputs to be added passthrough individual capacitors to a common point to which is alsoconnected the feedback resistor of the amplifier. A capacitor isconnected across the feedback resistor.

The voltage doubling circuit used in the blocks 26, 28, 30 and 32 ofFIG. 1 is shown in greater detail in FIG. 2. The transformer T and thediodes CR1 and CR2 provide full-wave rectification of the 400 c/sresolved signal and the full-wave rectified signal then passes throughan 800 c./s. band-pass filter formed by the resistors R26, R28 and R30and the capacitors C14 and C16. The values of the resistors R26, R28 andR30 depend upon the center frequency of the band-pass filter. Thecapacitor C16 is in the feedback circuit of an integrated-circuitdifferential amplifier X6 of the kind available under the designationType 741.

The trigger circuit or zero-crossing detector is shown in FIG. 3. Thiscircuit includes an integrated-circuit differential amplifier X10 of thekind available under the designation Type 709. The capacitor C26 and C27are stabilizing components which eliminate any tendency for theamplifiers to oscillate during the output voltage transitions. Anamplifier of the kind indicated has an open-loop gain such that theoutput will change from full negative to full positive for adifferential input voltage change of l or 2 millivolts. The capacitorC24 and the resistor R46 decouple any DC component from the precedingfrequency doubling circuit and the voltage across R46 is therefore asine wave symmetrical about 0V. The input impedance of differentialamplifier X10 is very high and the voltage on the inverting input is 0V.Consequently the output of amplifier X10 is a square wave switching atthe zero crossing points of the sine wave input. The transitions in thesine wave contain the phase information which is required.

The bistable circuit 38 and the field-effect transistor switches areshown in FIG. 4. The bistable circuit 38 includes two cross-coupledtransistors 05 and Q7, two input transistors Q3 and Q10, and two outputtransistors Q2 and Q9. The transistor Q3 receives its input signaldirectly from the trigger circuit 36. The transistor 010 receives itsinput signal from the trigger circuit 34 through the set-zero delaycircuit 40, which will be described later. The output of this delaycircuit is a square waveform identical to the output of trigger circuit34 but with its phase delayed by an adjustable amount.

Thus, the output of the bistable circuit is a pulse train with arepetition frequency of 1,600 pulses per second and a markspace ratiowhich depends upon the value of the angle d). The transistors 02 and Q9at the outputs of the bistable circuit trigger two field-effecttransistors Q13 and Q14 alternately. The drain electrode of thetransistor Q13 and the source electrode of the transistor Q14 areconnected to one end of a common load resistor R82 and the transistorsQ13 and Q14 provide the resistor 82 with an input waveform switchingbetween precise +1 volt and 1 volt levels, the mark-to-space ratio ofthis waveform being determined by the rotor position. The voltages forthe field-effect transistors are derived from differential amplifiersX13, X15 and X16. The amplifier X13 has a zener diode CR14 between itsnoninverting input and ground and the circuit forms a conventional zenerreference circuit with an output potentiometer RV4 providing anadjustable negative output. The differential amplifier X15 is a bufferfor this negative output and the differential amplifier X16 provides thedirect positive equivalent of this output. In this way the positive andnegative voltage reference lines for the field-effect transistorswitches are set up. Amplifiers X15 and X16 are of the kind known asType 741.

The resistor R82 at the output of the two field-effect transistorswitches has its other end connected through resistor R83 to thenoninverting input of a Type 741 differential amplifier X17. A feedbackcapacitor C42 is connected to the junction of the resistors R82 and R83and a feedback resistor R86 extends to the inverting input of theamplifier. The components around the amplifier act to filter out the DCcomponent of the waveform at the front end of resistor R82.

From the output of the lowpass output filter 50 there is obtained a DCvoltage representing the angle 4:.

The set-zero delay circuit will now be described. The transistors Q1, Q4and 06 (FIG. 5) form a short-pulse generator which emits a pulsewhenever the output of trigger circuit 34 switches positive. The pulsefrom transistor Q6 switches on the field-effect transistor Q12 for shortperiods to discharge capacitor C37. The voltage at the base oftransistor Q8 is controlled by the zener diode CR12 and this transistoracts to provide a constant current for charging capacitor C37. Thiscurrent reaches capacitor C37 by way of transistor Qll/l. The twotransistors Qll/l and 011/2 are in one package and are used as veryclosely matched diodes, back to back.

The peak voltage, reached at the instant prior to the discharging ofcapacitor C37 through transistor Q12, is stored on capacitor C38, whichit reaches by way of transistor Q11/2. The voltage stored on capacitorC38 is a function of the supply frequency and the charging current tocapacitor C37. This peak voltage goes to the noninverting input of aType 741 differential amplifier X12, the output of which is a DC voltagesimilar to that on capacitor C38. An adjustable fraction of this voltageis picked off at the wiper of potentiometer RV2, at the output ofamplifier X12, and is fed to the inverting input of the Type 709differential amplifier X14. The noninverting input of the amplifier X14is connected to the capacitor C37 and receives the ramp voltage acrossthe latter. Whenever the voltage across capacitor C37 reaches the valueof the voltage at the wiper of potentiometer RV2, the output ofamplifier X14 switches. The instant of switching can thus be adjustedand the adjustment effectively changes the mark-to-space ratio at theoutput of the bistable circuit in exactly the same way as would beproduced by rotating the synchro body.

This delay system has certain advantages. Firstly, a slow change in theconstant current output of transistor Q8 does not matter because thevoltage derived from amplifier X12 and the ramp voltage across capacitorC37 are directly related. Provided that the ramp voltage is linear, itsslope does not matter. Secondly, if the 400 c./s. input drifts slowlyabove or below the nominal frequency, the condition which causesamplifier X14 to switch is again such that the effective delay in termsof phase is unaltered.

Reverting to the frequency doubling facility, this is extremely usefulwhen the total angle of interest is never more than a small fraction of360 about a zero position. One example of this is where the angle ofelevons in an aircraft system is being indicated. The frequency doublingmethod makes possible the magnification of the angular movement withoutthe use of multipole synchros or of gear trains on single-pole-pairsynchros or of amplification of the basic electronic resolver output.The latter would amplify the errors together with the output signal and,what is more important, gives magnified output ripple which is oftenunacceptable. The frequency doubling proposed in the presentspecification eases the ripple problem.

. in the example shown, Scott-connected transformers are used. It wouldalso be possible to use star-delta resistor meshes but this imposes a DCearth reference on the synchro output lines. In the example shown, whensynchro resolver sources are used the transformers which areScott-connected for the synchro transmitters serve instead as simpleisolation transformers.

lclaim:

1. Apparatus for signalling the angular displacement Q5 of the rotor ofa synchro transmitter or resolver about an axis,

comprising:

means for deriving from the synchro transmitter or resolver first andsecond electric signals representing respectively sin wt sin 4; and sinwt cos d), where an is the phase angle of the supply for the synchrotransmitter or resolver;

phase-shifting means for deriving from the signal representing sin w!sin d) a third signal representing cos wt sin (b;

means for adding and subtracting the said second and third signals toobtain fourth and fifth signals representing iefit ljn sister slime,

means, including a comparator, responsive to the said fourth and fifthsignals to derive an output signal varying with the angle (45 and havinga full cycle of variation in a submultiple of a 360 variation of theangle (1:. 2. Apparatus for signalling the angular displacement 4a ofthe rotor of a synchro transmitter or resolver about an axis,comprising:

means for deriving from the synchro transmitter or resolver first andsecond electric signals representing respectively sin wt sin d) and sinwt cos qS, where out is the phase angle of the supply for the synchrotransmitter or resolver;

phase shifting means for deriving from the signal representing sin wtsin 41 a third signal representing cos mt sin 4);

means for combining the said second and third signals to obtain a fourthsignal representing the sine of the sum or difference of the angles wtand 1b;

frequency multiplying means connected to receive the fourth signal andto provide a frequency-multiplied signal representing the sine of thesum or difference of the angles nut and d), where n is the ratio of thefrequency multiplier; and

means, including a comparator, responsive to the saidfrequency-multiplied signal and to a further signal representing atrigonometric function of an angle varying with the angle wt to derivean output signal varying with the angle 11) and have a full cycle ofvariation in a submultiple of a 360 variation of the angle d).

3. Apparatus in accordance with claim 2, in which the saidsignal-combining means provides a signal representing sin (z+d signalrepresenting sin n tZF) the apparatus including a fln'thersignal-combining means to provide a signal representing sin (HF) andfurther frequency-multiplying means to provide a signal representingsin(n wt/F) the said comparator being connected to respond to thesignals sin (nwtZF) and sininwtlF).

4. Apparatus for signalling the angular displacement d1 of the rotor ofthe synchro transmitter or resolver about an axis, comprising:

means for deriving from the synchro transmitter or resolver first andsecond electric signals representing sin wt sin 4) and sinwr cos 45,where wt is the phase angle of the supply for the synchro transmitter orresolver; phase-shifting means for deriving from the signal representingsinwt sin :12 a third signal representing cosw! sin q);

means for combining the said second and third signals to obtain a fourthsignal representing the sine of the sum or difference of the angles wtand dz;

further means, including a comparator, responsive to the said fourthsignal and. to a further signal representing a trigonometric function ofan angle varying with the angle wt to derive an output signal varyingwith the angle 42 and having a full cycle of variation in a submultipleof a 360 variation of the angle and I zero-setting means connected inthe input circuit of the said comparator to receive the said fourthsignal prior to its application to the comparator.

5. Apparatus in accordance with claim 4, in which the zero- 5 settingcircuit includes a pulse generator connected to receive the saidresultant signal and to generate a pulse for each cycle of the supplyfrequency with a phase dependent on the said rotor angle; a capacitanceand a charging circuit for the capacitance; a discharge circuit for thecapacitance controlled I by the said pulse generator, so that thecharging cycle of the capacitance is synchronized with the operation ofthe pulse generator; and a comparator for comparing the voltage level atsaid capacitor with an adjustable reference level and for generating apulse train having a mark-to-space ratio controlled by the relationshipbetween the two compared signals, whereby zero-setting for the apparatusis efiected by adjustma tefths sai fstsesslexels pp xy l ss f base rstar ts 8. Apparatus for signalling the angular displacement d) of therotor of a synchro transmitter or resolver about an axis, comprising:

means for deriving from the synchro transmitter or resolver first andsecond electric signals representing respectively sinwt sin (b and sinwtcos where an is the phase angle of the supply for the synchrotransmitter or resolver;

phase-shifting means for deriving from the first signal a third signalrepresenting cos wt sin (b, the phase-shifting means including anintegrator circuit connected to receive the said first signal and aseries circuit comprising an inverter and a differentiator circuit alsoconnected to receive the said first signal;

signal-combining means connected to receive the outputs of theintegrator circuit and the said series circuit and the first signal forderiving a fourth signal representing the sine of the sum or differenceof the angles wt and d); and

6. Apparatus in accordance with claim 5, in which said means, includinga cnmparat or, responsive to the said wt to derive an output signalvarying with the angle 4, and

fourth signal and to a further signal representing 3 having 8 full cycleOf variation in a sub multiple Of a 360 L 92m sigw 2 mw an is yaaxiawhfih ma angle

1. Apparatus for signalling the angular displacement phi of the rotor ofa synchro transmitter or resolver about an axis, comprising: means forderiving from the synchro transmitter or resolver first and secondelectric signals representing respectively sin omega t sin phi and sinomega t cos phi , where omega t is the phase angle of the supply for thesynchro transmitter or resolver; phase-shifting means for deriving fromthe signal representing sin omega t sin phi a third signal representingcos omega t sin phi ; means for adding and subtracting the said secondand third signals to obtain fourth and fifth signals representing sin(omega t+ phi ) and sin( omega t- phi ); and means, including acomparator, responsive to the said fourth and fifth signals to derive anoutput signal varying with the angle phi and having a full cycle ofvariation in a submultiple of a 360* variation of the angle phi . 2.Apparatus for signalling the angular displacement phi of the rotor of asynchro transmitter or resolver about an axis, comprising: means forderiving from the synchro transmitter or resolver first and secondelectric signals representing respectively sin omega t sin phi and sinomega t cos phi , where omega t is the phase angle of the supply for thesynchro transmitter or resolver; phase shifting means for deriving fromthe signal representing sin omega t sin phi a third signal representingcos omega t sin phi ; means for combining the said second and thirdsignals to obtain a fourth signal representing the sine of the sum ordifference of the angles omega t and phi ; frequency multiplying meansconnected to receive the fourth signal and to provide afrequency-multiplied signal representing the sine of the sum ordifference of the angles n omega t and phi , where n is the ratio of thefrequency multiplier; and means, including a comparator, responsive tothe said frequency-multiplied signal and to a further signalrepresenting a trigonometric function of an angle varying with the angleomega t to derive an output signal varying with the angle phi and have afull cycle of variation in a submultiple of a 360* variation of theangle phi .
 3. Apparatus in accordance with claim 2, in which the saidsignal-combining means provides a signal representing sin(t+ phi ) andthe frequency-multiplying means provides a signal representing sin(n t+phi ), the apparatus including a further signal-combining means toprovide a signal representing sin (t-phi ) and furtherfrequency-multiplying means to provide a signal representing sin(n omegat- phi ), the said comparator being connected to respond to the signalssin(n omega t+ phi ) and sin(n omega t- phi ).
 4. Apparatus forsignalling the angular displacement phi of the rotor of the synchrotransmitter or resolver about an axis, comprising: means for derivingfrom the synchro transmitter or resolver first and second electricsignals representing sin omega t sin phi and sin omega t cos phi , whereomega t is the phase angle of the supply for the synchro transmitter orresolver; phase-shifting means for deriving from the signal representingsin omega t sin phi a third signal representing cos omega t sin phi ;means for combining the said second and third signals to obtain a fourthsignal representing the sine of the sum or difference of the anglesomega t and phi ; further means, including a comparator, responsive tothe said fourth signal and to a further signal representing atrigonometric function of an angle varying with the angle omega t toderive an output signal varying with the angle phi and having a fullcycle of variation in a submultiple of a 360* variation of the angle phi; and zero-setting means connected in the input circuit of the saidcomparator to receive the said fourth signal prior to its application tothe comparator.
 5. Apparatus in accordance with claim 4, in which thezero-setting circuit includes a pulse generator connected to receive thesaid resultant signal and to generate a pulse for each cycle of thesupply frequency with a phase dependent on the said rotor angle; acapacitance and a charging circuit for the capacitance; a dischargecircuit for the capacitance controlled by the said pulse generator, sothat the charging cycle of the capacitance is synchronized with theoperation of the pulse generator; and a comparator for comparing thevoltage level at said capacitor with an adjustable reference level andfor generating a pulse train having a mark-to-space ratio controlled bythe relationship between the two compared signals, whereby zero-settingfor the apparatus is effected by adjustment of the said reference level.6. Apparatus in accordance with claim 5, in which said reference levelis derived from a potentiometer the supply voltage for which is derivedfrom the charging circuit for the capacitor, whereby changes in thecharging current for the capacitor are prevented from affecting thezero-setting operation.
 7. Apparatus in accordance with claim 6,comprising a second capacitance connected to receive the peak voltage ofthe first capacitance and a circuit responsive to the voltage on thesecond capacitance and connected for controlling the supply voltage forthe said potentiometer.
 8. Apparatus for signalling the angulardisplacement phi of the rotor of a synchro transmitter or resolver aboutan axis, comprising: means for deriving from the synchro transmitter orresolver first and second electric signals representing respectively sinomega t sin phi and sin omega t cos phi , where omega t is the phaseangle of the supply for the synchro transmitter or resolver;phase-shifting means for deriving from the first signal a third signalrepresenting cos omega t sin phi , the phase-shifting means including anintegrator circuit connected to receive the said first signal and aseries circuit comprising an inverter and a differentiator circuit alsoconnected to receive the said first signal; signal-combining meansconnected to receive the outputs of the integrator circuit and the saidseries circuit and the first signal for deriving a fourth signalrepresenting the sine of the sum or difference of the angles omega t andphi ; and means, including a comparator, responsive to the said fourthsignal and to a further signal representing a trigonometric function ofan angle varying with the angle omega t to derive an output signalvarying with the angle phi and having a full cycle of variation in asubmultiple of a 360* variation of the angle phi .